"We must stop the madness, my friends," Mr. Cuomo said, offering a seven-point gun-control agenda that includes "the toughest assault-weapons ban in the country," elimination of the so-called "gun-show loophole," a ban on high-capacity magazines and ammunition sales over the Internet.

"We need a gun policy in this state that is reasonable, that is balanced, that is measured," Mr. Cuomo continued. "We respect hunters and sportsmen. This is not about taking away people's guns … it's about ending the unnecessary risk of high-capacity assault rifles."

His proposals come as the debate over gun control continues in the nation's capital. Vice President Joseph R. Biden on Wednesday convened his select panel to study the issue and make recommendations to President Obama. The vice president also met with the families of victims of gun violence, something Mr. Cuomo and Mr. Malloy have done recently on the heels of shootings in their states.

For Mr. Cuomo, it was the ambush of Webster. N.Y., firefighters on Christmas Eve, an assault that killed two and wounded two others. For Mr. Malloy, it was the horrific Dec. 14 shooting at Sandy Hook Elementary School in Newtown, which claimed the lives of 20 young children and six adults.

Mr. Malloy was still visibly shaken when he took to the stage Wednesday afternoon for his State of the State address, pausing several times and fighting back tears.

"When it comes to preventing future acts of violence in our schools, let me say this: More guns are not the answer. Freedom is not a handgun on the hip of every teacher, and security should not mean a guard posted outside every classroom," Mr. Malloy said, rejecting suggestions offered by Virginia Gov. Bob McDonnell, the National Rifle Association and others that either teachers be armed or that trained security guards protect each school building in America.

Mr. Malloy's sadness when talking about Sandy Hook quickly turned into a look of determination as he scolded those who think increased access to firearms is the answer.

"That is not who we are in Connecticut, and it is not who we will allow ourselves to become," he said, drawing a standing ovation from those gathered at the Statehouse in Hartford. "We also know that this conversation must take place nationally. As long as weapons continue to travel up and down [Interstate] 95, what is available for sale in Florida can have devastating consequences here in Connecticut."

Governors from the other side of the aisle also appear willing to engage in that national conversation, which quickly has become a top policy priority for the White House.

New Jersey Gov. Chris Christie, a potential Republican presidential candidate in 2016, said Wednesday that he's prepared to sit down and discuss stronger gun-control measures.

"These are complicated issues. I'm willing to have that conversation," Mr. Christie said.

He added that lawmakers at both the state and federal levels must address mental-health issues, violent video games and related issues in addition to any discussion about limiting Second Amendment rights.

While Mr. Christie may be willing to have the conversation, many other Republicans are not. Members of Congress have expressed real skepticism about the White House's gun-control agenda, and the NRA — one of the most effective and influential lobbying groups in Washington — has come out strongly against any restrictions on firearms.

That resistance can also be found in New York and Connecticut, ensuring that the governors of those states that, despite the recent shootings, that passing gun controls will still require a fight.

"The governor and others are politicizing the tragedy in Newtown to advance their anti-Second Amendment agenda. We need to take a real look at school safety and our state's mental health services, not declare war on the Second Amendment," said New York Assemblyman Kieran Michael Lalor, a Marine and former candidate for U.S. Congress. "The governor's proposals are not about making kids safe. They are about a political agenda."